Diagnosis of Weibel instability evolution in the rear surface density scale lengths of laser solid interactions via proton acceleration

It is shown for the first time that the spatial and temporal distribution of laser accelerated protons can be used as a diagnostic of Weibel instability presence and evolution in the rear surface scale lengths of a solid density target. Numerical modelling shows that when a fast electron beam is injected into a decreasing density gradient on the target rear side, a magnetic instability is seeded with an evolution which is strongly dependent on the density scale length. This is manifested in the acceleration of a filamented proton beam, where the degree of filamentation is also found to be dependent on the target rear scale length. Furthermore, the energy dependent spatial distribution of the accelerated proton beam is shown to provide information on the instability evolution on the picosecond timescale over which the protons are accelerated. Experimentally, this is investigated by using a controlled prepulse to introduce a target rear scale length, which is varied by altering the time delay with respect to the main pulse, and similar trends are measured. This work is particularly pertinent to applications using laser pulse durations of tens of picoseconds, or where a micron level density scale length is present on the rear of a solid target, such as proton-driven fast ignition, as the resultant instability may affect the uniformity of fuel energy coupling. (paper)